No big Afro wig, no loud guitars, no Mick Jagger.

Lisa Fischer, backup singer extraordinaire for the Rolling Stones, arrived on the stage of the Dakota Jazz Club Tuesday, kicked off her sandals and declared this to be her living room.

Then she delivered an extraordinary evening of art songs, not arena rock, of whispers, not wails, of enrichment, not excitement. Unless your idea of excitement is deeply intellectual, deeply soulful, deeply meditative music — one strikingly imaginative interpretation of a song (famous or obscure) after another.

Take “Wild Horses,” which often felt like a toss-off country plaint when Jagger did it. Fischer remounted “Wild Horses” as a song of quiet strength and determination, all the while showcasing her wondrous voice as she effortlessly glided from a high operatic note to a low-down spiritual moan, then to a soul tangent, a Gregorian-like chant and back to a spiritual embrace. Lisa Fischer can definitely drag you away.

Now 56, she released her first solo album in 1991 and won a Grammy but then opted for the life of a backup singer, with Luther Vandross, Tina Turner, Sting and others. She’s performed on every Stones tour since 1989. Then, in 2012, she unintentionally stole the show in the Oscar-winning documentary about backup singers, “20 Feet from Stardom.” Finally this year, she has undertaken her first solo tour ever.

She performed at the Dakota for one night in September and now, after touring Australia and New Zealand with the Stones, she has returned to Minneapolis for a three-night engagement with her mostly acoustic trio.

If she’s a sexy glamazon onstage with the Stones, on her own she’s a beatific earth-mother, wearing a stocking cap (not a wig), ditching the stiletto boots for barefeet and dialing down the volume and often singing without a microphone. But her repertoire still draws heavily from the Stones (“it’s like playing with the boys’ toys”).

However, she opened Tuesday’s 85-minute first set with a breathtaking reading of Amy Grant’s “Breath of Heaven.” After beginning with a wordless coo, the physically demonstrative Fischer eventually increased the intensity, but not the volume, as she turned a vaguely religious piece into a spare, almost jazzy meditation.

With her fertile imagination, she transformed Eric Bibb’s “Don’t Ever Let Nobody Drag Your Spirit Down” into a minimalist blues, Railroad Earth’s “Bird in the House” into a joyous, acoustic flight and Led Zeppelin’s “Rock and Roll” into the kind of rhythmic R&B-hued funk that Jimmy Page always envisioned.

One cover misfired, largely because the song — “Sing to the Moon” by little known British soul siren Laura Mvula from 2013 — was one-dimensional, repetitious and just not dynamic enough.

The most special moments came when Fischer recast the Stones hits. Thanks to J.C. Maillard’s work on a custom-made acoustic instrument inspired by the Turkish saz, “Jumpin’ Jack Flash” had the kind of slow Middle Eastern vibe that Robert Plant has mined. Fischer’s take on “Gimme Shelter” was not ominous but rather a plea for love, with a taste of Anita Baker’s “Sweet Love” woven in. Fischer flipped the gender on “Satisfaction” (she couldn’t get any “boy reaction” instead of “girly action”) and playfully proved that she can move like Jagger — her rooster-bobbing head, that Tina-like strut and those puckered lips.

Still, the most spectacular performance was Fischer’s own hit “How Can I Ease the Pain,” which resided where jazz, meditation, art-song and soul intersect. The six-minute song felt like an hour-long massage, making you feel relaxed and wanted. That’s because Fischer, who has remarkable control and incomparable musical range, does something better than any other singer: She consistently gets lost in her songs and takes listeners along with her.